# Interpreting log transformations in a logistic regression

This stats.stackexchange post contains explanation of how to interpret transformed variables in linear regression.

In particular, I found this snippet in Graham Cookson's answer (2nd answer):

Y and X -- a one unit increase in X would lead to a 𝛽

increase/decrease in Y

Log Y and Log X -- a 1% increase in X would lead to a 𝛽

% increase/decrease in Y

Log Y and X -- a one unit increase in X would lead to a 𝛽∗100

% increase/decrease in Y

Y and Log X -- a 1% increase in X would lead to a 𝛽/100 increase/decrease in Y

My question is, what would the equivalent interpretations be when the context is a logistic regression and not a linear regression? Since you cannot transform the dependent variable in binary classification, it's really the last one that I'm interested in: Y and Log X -- a 1% increase in X would lead to a 𝛽/100 increase/decrease in Y

If 2 input variables are log transformed and one has a resulting odds ratio 2 and one of 0.5, how can these be interpreted from a model explain-ability standpoint?

• And also, same question but for a quadratic predictor? – Doug Fir Mar 17 at 21:19